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Terminating Calculi for Propositional Dummett Logic with Subformula Property

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Abstract

In this paper we present two terminating tableau calculi for propositional Dummett logic obeying the subformula property. The ideas of our calculi rely on the linearly ordered Kripke semantics of Dummett logic. The first calculus works on two semantical levels: the present and the next possible world. The second calculus employs the semantical levels of known or not known at the present state of knowledge, that are usual in tableau systems, and exploits a property of the construction of the completeness theorem to introduce a check which is an alternative to loop check mechanisms.

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  1. Dipartimento di Informatica, Sistemistica e Comunicazione, Università di Milano-Bicocca, Piazza dell’Ateneo Nuovo, 1, 20126, Milano, Italy

    Guido Fiorino

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  1. Guido Fiorino
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Correspondence to Guido Fiorino.

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Fiorino, G. Terminating Calculi for Propositional Dummett Logic with Subformula Property. J Autom Reasoning 52, 67–97 (2014). https://doi.org/10.1007/s10817-013-9276-7

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  • DOI: https://doi.org/10.1007/s10817-013-9276-7

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